Galadriel is the daughter of Finarfin and the granddaughter of Finwë. Finwë was one of the first born of the elves and a king of Noldor, one of the 3 houses of the elves.  The Noldor journeyed to Valinor 3 ages before the Sun. Living on Valinor during the time of the Two Trees, gave the Noldor a certain kind of special power not particularly tangible, but making them stronger and more powerful than the elves that never left Middle Earth, but not more powerful than Maia. Galadriel was born in Valinor under the light of the Trees giving her am enduring power, beyond that of most elves. She was also a Queen being the granddaughter of Finwë. As far as immortality goes, all elves are immortal with 2 exceptions: they can be slain as in battle, though that is not so easy, and they can parish from great despair and grief which is why they love and cherish poetry and song.

Gandalf is a Maia, a sort of God since the Maia, spirits that descended into Arda (the World), are of the Ainur (Spirit Gods), but of lesser stature than the Valar. This makes him completely  immortal. All wizards are Maiar, so is Sauron and the Balrogs. and many others, some in human form and some not, some in Middle Earth and some not. Each has his or her own individual type of power and are sort of students of certain Valar, most poserful among the Ainur. Gandalf was of Manwë and Varda. [side note: Manwë is King of all the Valar. Varda is spouse of Manwë anda Queen of the Valar. She set the stars in the sky. That is why the elves call her Elbereth.]

Gandalf was the bearer of Narya (called the Red Ring and the Ring of Fire), one of the 3 great rings of power held by the elves, It was given to him by Círdan, an elf lord of the grey Havens, to aid him against Sauron. Galadriel was the bearer of Nenya (called The Ring of Water and the Ring of Adamant.) and used to maintain the land of Lórien. The 3 Rings of the Elves were made by Made by Celebrimbor and were never touched by Sauron and were never tainted by his evilness. However, should he have gotten his Ring back, he would have gained power over the Three rings and then all hope would have been lost for Middle Earth.